Chapter 8.2, Problem 14E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# Find the exact area of the surface obtained by rotating the curve about the x-axis.14. x = 1 + 2y2, 1 ≤ y ≤ 2

To determine

To find: The exact area of the surface obtained by rotating the curve about x-axis.

Explanation

Given information:

The equation of the curve is x=1+2y2,1â‰¤yâ‰¤2 .

The curve is bounded between y=1 and y=2 .

Calculation:

Show the equation of the curve.

x=1+2y2 (1)

Calculate the area of the surface obtained by rotating the curve about x-axis using the relation:

S=âˆ«cd2Ï€y1+(dxdy)2dy (2)

Here, S is the area of the surface obtained by rotating the curve about x-axis and

câ‰¤yâ‰¤d .

Differentiate both sides of Equation (1) with respect to y.

dxdy=ddy(1+2y2)=(0+4y)=4y

Substitute 4y for dxdy , 1 for c, and 2 for d in Equation (2).

S=âˆ«122Ï€y1+(4y)2dy=âˆ«122Ï€y1+16y2dy (3)

Consider the value of the function u=1+16y2 (4)

Calculate the upper limit of the function u using Equation (4).

Substitute 2 for y in Equation (4).

u=1+16Ã—22=65

Calculate the lower limit of the function u using Equation (4).

Substitute 1 for y in Equation (4).

u=1+16Ã—12=17

Differentiate both sides of the Equation (4) with respect to y

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started